Advice 1: How to find side using sine

Side of the triangle can be found not only on perimeter and area, but on a given side and corners. For this purpose trigonometric functions - sine and cosine. The problem with their use meet in the school geometry course, as well as in the College course of analytical geometry and linear algebra.
How to find side using sine
Instruction
1
If you know one of the sides of a triangle and the angle between it and the other party, use the trigonometric functions - sineom Kosineohms. Imagine a right triangle HBC , which angle α is 60 degrees. Triangle HBC is shown in the figure. Since the sine, as you know, is the ratio of the opposite leg to the hypotenuse, andthe sine - ratio of the adjacent leg to the hypotenuse, to solve this problem, use the following relation between these parameters:sin α=NV/Sootvetstvenno, if you want to know the side of a right triangle, let's Express it using the hypotenuse as follows:HB=BC*sin α
2
If the problem, on the contrary, given side of a triangle, find the hypotenuse, according to the following ratio between the specified values:BC=HB/sin APO analogy, find the sides of the triangle and using tosineand changing the previous expression in the following way:cos α=HC/BC
3
In elementary mathematics there is the concept of the theorem is the sine ofs. Guided by the facts which describes this theorem, you can also find the sides of the triangle. In addition, it allows you to find the sides of a triangle inscribed in a circle if the radius is known is known to last. Use the ratio specified below:a/sin of α=b/sin b=c/sin y=2RЭта theorem applicable in the case when given two sides and angle triangle, or given one of the angles of a triangle and the radius described around the circumference.
4
An addition theorem of the sine ofs, and exist in substantially the theorem forthe sine ofs, which, like the previous one, also applies to the triangles in all three varieties: right angle, acute and obtuse. Guided by the facts, which prove this theorem, we can find the unknown values using the following relationship:c^2=a^2+b^2-2ab*cos α

Advice 2 : What is the sine and cosine

The study of triangles being mathematicians for several millennia. The science of triangles - trigonometry - uses special values: sine and cosine.
What is the sine and cosine

Right triangle


Initially, the sine and cosine arose from the need to calculate values in right triangles. It was observed that if the value of the degree measures of the angles in a right triangle do not change, the aspect ratio, no matter how these parties are neither changed in length, remains always the same.

And it was introduced the concepts of sine and cosine. The sine of an acute angle in a right triangle is the ratio of the opposite leg to the hypotenuse, cosine – adjacent to the hypotenuse.

Cosines and sines


But the cosines and sines can be applied not only in right triangles. To find the value of the obtuse or acute angle, the sides of any triangle, it is enough to apply theorem law of cosines and law of sines.

The theorem of the cosines is quite simple: the squares of the sides of a triangle is equal to the sum of the squares of the other two sides minus twice the product of these sides into the cosine of the angle between them."

There are two interpretations of the theorem of sines: small and extended. According to small: "In a triangle the angles opposite the sides are proportional". This theorem often extend through the properties of a triangle circumscribed about the circle: In a triangle the angles opposite the sides are proportional and their ratio is equal to the diameter of the circumscribed circle".

Derivatives


The derivative is a mathematical tool that indicates how quickly changes in the function of relative change of its argument. Derivatives are used in algebra, geometry, Economics and physics, the number of technical disciplines.

When solving problems you must know the table values of the derivatives of trigonometric functions: sine and cosine. The derivative of sine is cosine, and cosine - sine, but with the sign "minus".

Application in mathematics


Very often the sines and cosines are used when solving right-angled triangles and problems associated with them.

The convenience of sines and cosines is reflected in the technique. Corners and sides were just judged by the theorems of cosines and sinuses by breaking up the complex shapes and objects with "simple" triangles. Engineers and architects, often dealing with the calculations of the aspect ratio and degree measures, spending a lot of time and effort to calculate the cosines and sines of angles is not tabular.

Then "help" came to the table Bradis containing thousands of values of sines, cosines, tangents and cotangent different angles. In Soviet times, some teachers were forced to teach their charges page tables Bradis by heart.
Is the advice useful?
Search